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Reason's Nearest KinPhilosophies of Arithmetic from Kant to Carnap$
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Michael Potter

Print publication date: 2002

Print ISBN-13: 9780199252619

Published to Oxford Scholarship Online: May 2007

DOI: 10.1093/acprof:oso/9780199252619.001.0001

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Conclusion

Conclusion

Chapter:
(p.278) Conclusion
Source:
Reason's Nearest Kin
Author(s):

Michael Potter (Contributor Webpage)

Publisher:
Oxford University Press
DOI:10.1093/acprof:oso/9780199252619.003.0013

This concluding chapter summarizes the discussion in the preceding chapters. The book sought an answer to the question: can we give an account of arithmetic which does not make it depend for its truth on the way the world is? And if so, what constrains the world to conform to arithmetic? All the accounts we have considered have turned out to be flawed. But what is striking is how often an account was rejected not for philosophical reasons but for technical ones. It is shown that since the problem of arithmetic participates in the larger puzzle of the relationship between thought, language, experience, and the world, we can distinguish accounts that look to each of these to supply the content we require.

Keywords:   arithmetic, language, Kant, Frege, Hilbert, Dedekind, Wittgenstein, Ramsey, Gödel, Carnap

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